Box-Cox변환을 이용한 다변량 공정능력 분석
Analysis of Multivariate Process Capability Using Box-Cox Transformation
3
조회
0
다운로드
2
인용
0
참고문헌
키워드
초록
The process control methods based on the statistical analysis apply the analysis method or mathematical model under the assumption that the process characteristic is normally distributed. However, the distribution of data collected by the automatic measurement system in real time is often not followed by normal distribution. As the statistical analysis tools, the process capability index (PCI) has been used a lot as a measure of process capability analysis in the production site. However, PCI has been usually used without checking the normality test for the process data. Even though the normality assumption is violated, if the analysis method under the assumption of the normal distribution is performed, this will be an incorrect result and take a wrong action. When the normality assumption is violated, we can transform the non-normal data into the normal data by using an appropriate normal transformation method. There are various methods of the normal transformation. In this paper, we consider the Box-Cox transformation among them. Hence, the purpose of the study is to expand the analysis method for the multivariate process capability index using Box-Cox transformation. This study proposes the multivariate process capability index to be able to use according to both methodologies whether data is normally distributed or not. Through the computational examples, we compare and discuss the multivariate process capability index between before and after Box-Cox transformation when the process data is not normally distributed.
Abstract
The process control methods based on the statistical analysis apply the analysis method or mathematical model under the assumption that the process characteristic is normally distributed. However, the distribution of data collected by the automatic measurement system in real time is often not followed by normal distribution. As the statistical analysis tools, the process capability index (PCI) has been used a lot as a measure of process capability analysis in the production site. However, PCI has been usually used without checking the normality test for the process data. Even though the normality assumption is violated, if the analysis method under the assumption of the normal distribution is performed, this will be an incorrect result and take a wrong action. When the normality assumption is violated, we can transform the non-normal data into the normal data by using an appropriate normal transformation method. There are various methods of the normal transformation. In this paper, we consider the Box-Cox transformation among them. Hence, the purpose of the study is to expand the analysis method for the multivariate process capability index using Box-Cox transformation. This study proposes the multivariate process capability index to be able to use according to both methodologies whether data is normally distributed or not. Through the computational examples, we compare and discuss the multivariate process capability index between before and after Box-Cox transformation when the process data is not normally distributed.
참고문헌 (13)
- Anderson, T. W., "A test of goodness of fit", Journal of the American Statistical Association, 49(268), pp.765~769 (1954)
- Box, G. E. P., "An Analysis of Transformations", Journal of the Royal Statistical Society, Series B, 26(2), pp.211~252 (1964)
- 장영순, "분포분할법을 이용한 휴리스틱 공정능력지수의 비교 분석", 품질경영학회지, 41(2), pp.233~246 (2013), 한국품질경영학회[DOI]
- Hosseinifard, S. Z., "A transformation technique to estimate the process capability index for non-normal processes", International Journal of Advanced Manufacturing Technology, 40, pp.512~517 (2009)
- Looney, S. W., "How to Use Tests for Univariate Normality to Assess Multivariate Normality", The American Statistician, 49(1), pp.64~70 (1995)
- 문혜진, "역정규 손실함수를 이용한 다변량 공정능력지수", 한국산업경영시스템학회지, 41(2), pp.174~183 (2018), 한국산업경영시스템학회[DOI]
- Razali, N. M., "Power comparisons of shapiro-wilk, kolmogorov-smirnov, lilliefors and anderson-darling tests", Journal of Statistical Modeling and Analytics, 2(1), pp.21~33 (2011)
- Royston, J. P., "Some Techniques for Assessing Multivarate Normality Based on the Shapiro-Wilk W", Journal of the Royal Statistical Society. Series C, 32(2), pp.121~133 (1983)
- Small, N. J. H., "Marginal Skewness and Kurtosis in Testing Multivariate Normality", Journal of the Royal Statistical Society. Series C, 29(1), pp.85~87 (1980)
- Taam, W., "A Note on Multivariate Capability Indices", Journal of Applied Statistics, 20, pp.339~351 (1993)
- Wu, C. H., "Box-Cox Transformation Approach for Evaluating Non-Normal Processes Capability Based on the Cpk Index", Journal of Testing and Evaluation, 42(4), pp.949~961 (2014)
- Yap, B. W., "Comparisons of various types of normality tests", Journal of Statistical Computation and Simulation, 81(12), pp.2141~2155 (2011)
- Zhang, T., "Box-Cox Transformation in Big Data", Technometrics, 59(2), pp.189~201 (2017)